KR102617225B1 - Method and control system using piston amplitude recovery for free piston machines - Google Patents

Abstract

A method and apparatus for detecting the displacement amplitude of an armature of a linear motor or alternator driveably coupled to a load or prime mover are disclosed. Both the method and the apparatus require only three inputs derived from the input terminals of the linear motor or alternator: (1) the voltage measured across the linear motor terminals; (2) Current consumed by the linear motor; (3) Phase between voltage and current. The three inputs are sensed at the terminals of a linear motor or alternator and used to perform mathematical calculations in the microcomputer of the control system or controller. The mathematical calculations are based on the equivalent circuit, which is a modification of the equivalent circuit for a linear motor or alternator. The detected displacement amplitude can be used by the controller to limit the displacement amplitude of the armature to prevent collisions.

Description

Method and control system using piston amplitude recovery for free piston machines

The present invention relates to both the control of a linear motor coupled to drive a load such as a free piston Stirling cooler, and the control of a linear alternator coupled to be driven by a prime mover such as a Stirling engine. More specifically, the present invention describes linear A method and device allows the displacement amplitude of a motor or alternator to be repeatedly detected. As a result, no electromechanical device is required to directly sense the displacement amplitude. The present invention enables calculations that can be performed within sufficiently short time intervals and that are simple enough to be performed with practical controller computing circuits for use in commercially available products. The mathematical expressions applied in the present invention are based on taking certain modifications of the motor or alternator circuit which simplify the calculations but introduce only minor and insignificant differences between the actual displacement amplitude and the calculated amplitude.

As used herein, the term "amplitude", when applied to a reciprocating mechanical structure such as a piston or armature, means the coefficient of the sine function that defines the periodic sinusoidal displacement of the mechanical structure as a function of time. Amplitude is usually referred to as half the stroke. Similarly, when applied to electrical parameters that alternate sinusoidally, such as voltage or current, "amplitude" means the coefficient of the sine function that defines the change in the instantaneous value of the electrical parameter as a function of time. Amplitude is referred to as half the peak-to-peak value. When the armature of a linear motor or alternator is drivably linked to another structure, for example, when the armature of a linear motor is linked to the piston of a Stirling cooler, the displacement amplitude of all linked components rigidly attached together is are identical in amplitude and phase. Because the components move together as a unit, they can be referenced and expressed mathematically as part of the armature. As is known to those skilled in the art, sinusoidally varying voltages and currents can be described by the amplitudes of the components or alternatively their root-mean-square values, abbreviated as rms values. These are constant coefficients It's so different. As a result, the voltages and currents described in this document can be defined as rms or amplitude.

Electric linear motors and linear alternators are commonly known devices for driving various mechanical loads in reciprocating motion or for converting the linear reciprocating motion of other types of prime movers into alternating current. Those skilled in the art recognize that linear motors and linear alternators are the same basic electrical and mechanical structure. Each has a stator, sometimes referred to as a primary, with electrical coil windings, and a reciprocating armature, sometimes referred to as a secondary actuator, slider or transducer.

In a similar way, a free piston Stirling machine having the same basic mechanical structure can be operated as a prime mover to drive other loads, including a linear alternator, by the application of a heat source, or driven by a prime mover including a linear motor. It can operate as a cooler or heat pump. A free piston Stirling machine has a reciprocating piston and a reciprocating displacer. The piston can be driven by a prime mover to operate as a cooler/heat pump, or the piston can be connected to a mechanical load and the Stirling machine can be operated as a motor. In this document, the term "combined machine" is used to refer to a linear motor driving a load such as a Stirling cooler and a linear alternator driven by a prime mover such as a Stirling engine. The invention is applicable to a variety of combination machines known in the art, but is illustrated, for example, as a linear motor driving a Stirling cooler.

The reciprocating amplitude of a linear motor or alternator and the piston reciprocating amplitude of a Stirling machine are not limited or limited by any motion conversion structures such as crankshafts and connecting rods. Instead, when the reciprocating armature of a linear motor or alternator is coupled to another machine, such as the reciprocating piston of a free-piston Stirling machine, all of the reciprocating components are aligned with the fixed components of one of the machines. It is “free” to oscillate over a range of displacement amplitudes limited only by the collision.

It is desirable to avoid collisions resulting from excessive displacement amplitudes of the reciprocating components of a free-piston coupled machine, as such collisions may damage or destroy either or both coupled machines. Using a linear motor or alternator coupled to a free piston Stirling machine, it is relatively easy to measure the displacement amplitude at which an impact occurs. This can be done by manually sliding the armature in both directions at low speed until a bump is felt or heard and recording the displacement. Knowledge of the minimum displacement amplitude (X _c ) at which a collision occurs allows the engineer to define a maximum displacement amplitude (X _max ) that is sufficiently smaller than the collision displacement amplitude (X _c ) at which a collision can be avoided. Consequently, in free piston coupled machines it is desirable to continuously detect the operating displacement amplitude (X) as an electrical data parameter proportional to the displacement amplitude. The displacement amplitude ( ) is particularly desirable.

As is well known, linear motors and alternators are devices commonly used to drive or transmit power from free piston machinery. The amplitude of the piston of a Stirling cooler is primarily determined by the voltage of the linear motor that drives it, but is also strongly influenced by the power consumed or delivered by the machine. Therefore, it is difficult to know the maximum possible voltage under all operating conditions because the driving voltage itself is not an exact function of the displacement amplitude. In the following, to simplify the prose, the invention will be described only in terms of power absorbing devices, with the view that the power producing devices are simply the opposite situation.

During start-up of a Stirling cooler, current practice often involves slowing down the terminals of the linear motor to prevent the linear motor from driving the piston of the Stirling cooler into collision with its mechanical stop (commonly referred to as overstroke). It relies on applying a rising driving voltage. In prior art controllers of Stirling coolers driven by linear motors, the steady-state operating voltage is typically stored in and retrieved from a look-up table. These techniques suffer from changing load conditions that change the behavior of the machine, and therefore the ramp time may not be sufficient to bring the machine to the required condition before full power is applied. An additional difficulty is that changes in mechanical properties due to wear or gas leakage lead to inaccurate voltage parameters. Of course, either way, it is possible to simply include in the design sufficient buffer area or clearance for piston movement to avoid the possibility of collision. However, this approach results in dead space or unused capacity because the power depends on the square of the piston amplitude. In applications such as deep-temperature freezers, it is important to obtain the fastest initial cooling and recovery after door opening to limit exposure of expensive freezer contents to extended temperature fluctuations. This can only be achieved by operating the free piston cooling machine at full capacity, which is also the maximum allowable piston amplitude. Therefore, it is desirable to bring the displacement amplitude of the piston of the Stirling cooler to its maximum amplitude as quickly as possible without causing any collision.

In U.S. Patent No. 5,342,176 R. W. Rediich describes a method of obtaining the piston amplitude by means of discrete components or by digitally providing an analog equivalent, i.e. essentially a simulation of a free piston device. Redlich's method provides piston amplitude named reconstruction method. However, solving the equations described, in this case the speed of the reciprocating piston, requires analog or digital integration. Although Rediich requires only two inputs, instantaneous voltage and current, the method of integration requires considerable computational power and time, and the numbers can be inaccurate.

To effectively control free piston machines driven by linear motors, the voltage for maximum piston amplitude must be adjusted under any load or machine condition so that the maximum power point is obtained without the piston exceeding its maximum amplitude (X _max ). It's important to know. As a result, for any changing load or changing machine conditions, it is possible to continuously detect the displacement amplitude ( It is preferred and is the object and feature of the present invention.

The present invention consists in a method and apparatus for detecting the displacement amplitude of an armature of a linear motor or alternator driveably coupled to a load or prime mover, under any operating conditions. Both the method and the apparatus require only three inputs derived from the input terminals of a linear motor or alternator: (1) the RMS or peak voltage measured across the linear motor terminals; (2) RMS or peak current consumed by the linear motor; and (3) the phase between voltage and current, which can be obtained from the power factor. The method senses these three inputs at the terminals of a linear motor or alternator and uses them to perform mathematical calculations on a microcomputer in a control system or controller. The mathematical calculations are based on the equivalent circuit, which is a particularly simplified modification of the equivalent circuit for a linear motor or alternator. The recovered or detected displacement amplitude is used by the controller or controller to limit the displacement amplitude of the armature to an amplitude (X _max ) smaller than the amplitude (X _c ) that would cause a collision of the reciprocating armature with the stationary part.

1 is an axial cross-sectional view of a linear motor, a component part of a coupled linear motor driving a free piston Stirling cooler illustrating an embodiment of the present invention.
Figure 2 is a schematic diagram of the linear motor of Figure 1.
Figure 3 is a circuit schematic diagram of an equivalent circuit for a linear alternator or linear motor as shown in Figures 1 and 2.
Figure 4 is a circuit schematic diagram of an equivalent circuit for a linear alternator or linear motor, a simplified modification of the circuit of Figure 3 and is the basis for explanation of the mathematical equations used for embodiments of the present invention.
Figure 5 is a circuit schematic diagram of an equivalent circuit for a linear alternator or linear motor, a further simplified modification of the circuit of Figure 4 and is the basis for explanation of the mathematical equations used for embodiments of the invention.
FIG. 6 is a phasor diagram showing the relationship between electrical parameters for the equivalent circuits of FIGS. 3 to 5.
Figure 7 is a graph of the magnet displacement amplitude recovered according to the invention based on the two equivalent circuits of Figures 4 and 5 against the measured amplitude.
Figure 8 shows an arrangement for applying the invention in a control circuit for a free piston Stirling cooler.
In describing the preferred embodiments of the invention shown in the drawings, specific terminology will be used for clarity. However, the present invention is not limited to the specific terms so selected, and each specific term should be understood to include all technical equivalents that operate in a similar manner to achieve a similar purpose. For example, the word "connected" or similar terms are often used. These are not limited to direct connections, but also include connections through other circuit elements recognized as equivalent by those skilled in the art. Additionally, circuits of the type that perform well-known operations on electronic signals are illustrated. Those skilled in the art will recognize that there are many alternative circuits that are recognized as equivalent because they provide the same operation on signals and that additional circuits may be added in the future.

In the following description, the magnet amplitude, piston amplitude and armature amplitude are all displacement amplitudes and are synonymous and have the same magnitude (value). The term “ideal” has a meaning associated with the practice of forming an equivalent circuit from lumped, idealized circuit elements, as is well known to those skilled in the art of circuit analysis.

Recognizing that the amplitude of the magnet is described by a substantially linear system and that the linear motor itself is substantially linear, it is possible to form an equivalent circuit from which the magnet amplitude can be extracted for a given applied voltage and current. From the voltage and current and their phase relationship to each other, it is possible to extract the ideal induced voltage of the motor. This ideal induced voltage (RMS or peak) is proportional to the amplitude of the magnet's velocity, and since the frequency is known, the amplitude can be calculated directly. The algorithm to do this is just a few lines of code and can be calculated after each cycle or after many cycles since the machine does not respond quickly to changes in load.

The following description begins with a description of the content of the drawings, followed by an analysis explaining the basis of the mathematical relationships used in the invention.

Figure 1 shows a cross-sectional view of a typical linear motor of the type designed by Redlich for use in free piston machines. Figure 2 is a schematic or outline drawing of the linear motor shown in Figure 1 using the same reference numerals in both figures. 1 and 2, the toroidal coil winding 10 within the iron core 12 crosses a radial air gap 14 perpendicular to the faces of the core 12 at the boundary of the air gap 14. generates a magnetic field. The reciprocating armature 11 has a ring 16 made of rectangular permanent magnets 18 (or ring permanent magnets) radially biased within an air gap 14. The magnets 18 move axially within the iron core 12 in response to an alternating voltage 15 applied to the winding terminals 13 (Figure 2) to drive a current through the coil 10 (Figure 2). 2). Coil 10 is shown on the outer ferrous part 20 of core 12. Alternatively, it is often convenient to place the windings within the internal ferrous part 22 of the core 12.

Figure 3 shows an equivalent circuit for a linear motor disclosed in the prior art by Redlich, Unger and van der Walt. R _s represents the losses due to eddy currents and hysteresis induced by the motion of the magnet with the coil winding open circuit. R _dc represents the resistance loss in the coil, and ΔR _extemal represents the inductive loss in the surrounding structure of the motor. L is the inductance of the motor mainly due to the coil windings. V _ind is the open circuit voltage induced by magnet motion, and V _appl is the applied terminal voltage. I and I _m are the terminal and motor currents, respectively.

Since Figures 3, 4 and 5 are equivalent circuits consisting of ideal circuit elements tied together, the only terminals available for a real linear alternator or motor are those of the voltage source (V _appl ). These are the alternator or motor terminals referred to in this detailed description. Those skilled in the art will recognize that there are techniques known to those skilled in the art for obtaining constant values representing the resistance and inductance circuit elements of the components of an equivalent circuit, for example from laboratory tests. The resistive losses described for linear motors of the prior art are well known. These constant values are stored in the controller's microcomputer and can be used for subsequent data processing.

Figure 4 shows a variation of the circuit of Figure 3, providing a practical equivalent circuit upon which the present invention is based. The equivalent circuit in Figure 4 provides a close approximation to the equivalent circuit in Figure 3. This modification is based on the observation that in practice the voltage across R _s is much larger than the voltage across R _dc + ΔR _extemal . This provides simplification as follows:

Voltage across R _s

Therefore, the practical equivalent circuit of Figure 4 is applicable to a good approximation. This circuit modification allows for simplification of the calculation of displacement amplitude.

Figure 5 shows a more simplified equivalent circuit. In the equivalent circuit of Figure 5, all losses induced due to magnet motion are bundled into the R _ac equivalent circuit resistance. Here, no energy dissipation occurs as a terminal open circuit, which leads to some additional inaccuracy. For the equivalent circuit of Figure 5, I _m = I.

Figure 6 shows the phasor relationship between voltage and motor current. The motor current is the current (I _m ) flowing through the windings of the coil 10. _where The resistance voltage is in phase with the current (I _m ), and the induced voltage is in quadrature with the current (I _m ).

Figure 7 shows a graph comparing the magnet displacement amplitude (X) recovered according to the invention based on the equations developed from the two equivalent circuits of Figures 4 and 5 with the actual measured displacement amplitude. Figure 7 shows how close the displacement amplitude (X) detected (recovered) according to the present invention is to the actual measured displacement amplitude. Line 24 represents the actual measured displacement amplitude. Line 26 (dotted line) represents the displacement amplitude (X) recovered (detected) according to the invention based on the equation developed from the equivalent circuit of Figure 4. Line 28 (dotted line) represents the displacement amplitude (X) recovered (detected) according to the invention based on the equation developed from the equivalent circuit of Figure 5.

Figure 8 shows a displacement amplitude recovery method implemented in a controller for a free piston Stirling cooler to obtain a signal representing the piston displacement amplitude (X) for use in a feedback control system. Most of the circuit arrangements shown in Figure 8 are known in the prior art. The elements of the prior art are first described in a summary manner since they are known to those skilled in the art. A free piston Stirling cooler 30 absorbs heat from the target 32 like a cryogenic freezer. The Stirling cooler 30 is internally configured with a linear motor 34 in its rear space. The component parts of the linear motor 34 are identical to those described in connection with FIGS. 1 and 2 and therefore the same reference numerals apply to these component parts. The piston 36 of the Stirling cooler is fixed to magnets 18 of a linear motor 34 which drives the piston 36 in a reciprocating motion within the cylinder 37 as a result of the alternating voltage applied to the coil 10. . As is known in the art of free piston Stirling machines, changes in pressure within the Stirling cooler cause the displacer 38 to reciprocate. The reciprocating motion of the displacer 38 forces the working gas in periodically alternating directions within the cylinder 37 through the regenerator 40. Heat is conducted from the target to the upper cold end of the Stirling cooler 30 and from the upper cold end of the Stirling cooler 30 to the heat exchanger 42 due to the periodic movement of the working gas combined with periodic pressure changes within the cylinder. Heat is transferred from the heat exchanger to the surrounding atmosphere. The periodic movement of the working gas combined with the periodic pressure changes within the cylinder causes heat to be pumped from the upper cold end of the Stirling cooler 30 and the target 32 to the heat exchanger 42. ) is transmitted to the surrounding atmosphere. The Stirling cooler also has a driver 44 that applies alternating voltage to the coil 10 of the linear motor 34. The amplitude of the driving voltage is controlled by the controller 46. Under steady-state operating conditions, according to the start-up sequence, the negative feedback control principle is applied to maintain the target temperature at the set temperature. For this purpose, the temperature sensor 43 applies a signal representing the target temperature to the summing connection 62, to which a signal representing the set temperature is also applied. The error between the two causes the driver 44 to change the voltage applied to the linear motor in a way to maintain the target temperature at the set temperature. All this is carried out according to long-established control principles and is typically carried out by digital processing.

To practice the invention, the piston displacement amplitude must be calculated according to mathematical operations described below. The piston displacement amplitude is recovered from the electrical parameters sensed at the coil terminal 13 available to the driver 44 as illustrated in block 48. _The recovered (detected) piston displacement amplitude The error signal from summing connection 50 is applied to a controller which limits the displacement amplitude not to exceed X _max .

Of course, as is known to those skilled in the art, performing all summation operations, voltage limit operations and calculations according to the equations is typically performed by digital processing within the controller. Modern controllers include microcomputers. The term "microcomputer" is used to identify a type of computing circuit commonly used in the prior art to perform computing operations on control circuits. It is not intended to refer to the alternative meaning of a desktop, laptop, or other form of user-interactive computer including peripheral equipment such as a monitor, keyboard, and mouse. Since the processing is performed by the controller's microcomputer, physical sensing devices and circuits electrically connected to the coil terminals to sense coil voltage and current produce I and V outputs, phase (power factor) and all other mathematical calculations are performed. It can be transmitted directly to a capable controller.

Now returning to the analysis that underlies the invention, a basic aspect of linear motor theory is that the induced voltage (V _ind ) is directly proportional to the magnet shaft speed (ωX), where ω is the frequency in radians per second and X is the displacement amplitude. . For a Stirling cooler driven by a linear motor, the frequency (ω) is the frequency of the AC voltage driving the linear motor, and is typically the resonant frequency of the coupled machine. The proportionality constant (α), commonly known to those skilled in the art as a motor constant with numerically equivalent units of volts per meter per second or newtons per ampere, allows the induced voltage to be written as equation 1:

[ Equation 1 ]

V _ind = αωX

Equation 1 shows that by obtaining or deducing V _ind and knowing α and ω, it is possible to obtain the magnet, and therefore armature, displacement amplitude (X).

Figure 1 shows a typical linear motor in which the armature 11 is caused to oscillate axially with amplitude X. Radially polarized magnets 18 are attached to the armature 18 and form part of it. The circumferential coil 10 windings provide alternating fields in the outer and inner iron core components 20 and 22 respectively. Coil 10 has electrical terminals 13. When an alternating voltage is applied to the terminals 13 of the coil 10, the stator field generated by the coil 10 crosses the air gap 14 between the iron core components 20, 22. The field in the air gap 14 interacts with the magnetic edge currents of the essentially cylindrical magnets 18 , causing the magnets 18 , and therefore the armature 11 , to oscillate in an axial direction (vertical in FIGS. 1 and 2 ). ) provides the power to move. This is schematically represented in Figure 2 where all elements are identified with the same symbols as in Figure 1. The alternating voltage applied to terminal 13 is V _appl .

In the equivalent circuit for a linear motor shown in Figure 3, R _s accounts for the eddy currents and hysteresis losses associated with the magnet movement due to the coil 10 open circuit. The DC resistance of coil 10 is described by R _dc , while the losses associated with the current induced in the support structure are denoted by ΔR _external . The inductance L is primarily associated with the coil 10 windings, but also includes small contributions from other sources, for example from the stator iron core components 20 and 22. When alternating voltage (V _appl ) is applied to terminal 13, current (I) flows. The induced open circuit voltage associated with magnet motion is V _ind .

In the following analysis, the peak value is used. The RMS value is the coefficient for voltage and current in Equation 2 below: It will function fine except that it needs to be applied.

From circuit analysis applied to the equivalent circuit of Figure 3, it is possible to obtain the induced voltage (V _ind ) in terms of terminal voltage and current as shown in equation 2:

Here, j is a virtual term represents.

It is certainly possible to use equation 2 to obtain the induced voltage (V _ind ) from the terminal voltage (V _appl ) and current (I), but computational power is not always conveniently available and cost-effective in small on-board microcomputers. will ask for

The actual equivalent circuit in Figure 4 is a very close approximation to the equivalent circuit in Figure 3 because the voltage across R _s is much greater than the voltage across R _dc + ΔR _external . Accordingly, R _s can be moved from its position in Figure 3 to its position in Figure 4 where it is shunted directly across the terminals 13 of the coil 10 of the linear motor. Current (I _m ) can be expressed as Equation 3:

[ Equation 3 ]

All other elements remain the same.

See Figure 6, which is a voltage-current phasor diagram for the motor. I _m is known from equation 3, and the voltage across the motor is V _appl for a practical equivalent circuit.

Power factor (pf), like voltage (V _appl ) and current (I), can be measured by any of several conventional devices, circuits and methods well known in the art. The simplest and most common method used in the prior art to determine power factor is to calculate the actual power (or true power) and then calculate the apparent power. The share of these two is the power factor.

From the power factor pf, the phase angle ϕ _pf between V _appl and I is obtained.

[ Equation 4 ]

ϕ _pf = cos ^-1 (pf)

Looking at the voltage-current relationship depicted by the phasor in Figure 6, and keeping in mind that V _m = V _appl , the components of V _ind can be calculated. One component is in the I direction and one component is perpendicular to the I direction (i.e., the direction perpendicular to the voltage across the inductor as a function of current (I)). As can be seen graphically in Figure 6 and using Equation 3, these components are calculated by Equation 5 and Equation 6.

[ Equation 5 ]

(Component in I direction)

[ Equation 6 ]

(Component at LωI _m perpendicular to the I _m direction)

Using Equation 1 and the Pythagorean theorem, the magnet (armature) amplitude follows the magnitude of the components of V _ind :

[ Equation 7 ]

These are accurate results, but will vary to some extent with changes in the motor constants due to temperature effects and/or other nonlinearities, which of course can be explained by appropriate and known functional relationships.

Therefore, knowing the phasor relationship between voltage and current in addition to the basic motor parameters makes it possible to extract (or recover) the magnet amplitude. This non-invasive means of determining amplitude is useful in control systems.

For the simple equivalent circuit of Figure 5, I _m = I and, as mentioned, inductive losses due to magnet motion are entirely taken care of by R _ac . The circuit of Figure 5 has slightly more stringent assumptions than the circuit of Figure 4, and these introduce some additional errors. For the circuit of Figure 5, the two voltage components of V _ind will be given by equations (8) and (9):

[ Equation 8 ]

(Component in I direction)

[ Equation 9 ]

(Component in LωI perpendicular to I direction)

The components calculated from Equation 8 and Equation 9 are applied to Equation 7 to obtain the magnet amplitude.

The recovered amplitudes of the real equivalent circuit in Figure 4 and the simple equivalent circuit in Figure 5 are plotted against the measured values of the magnet amplitude in Figure 7. The recovered amplitude correlation for the real equivalent circuit of FIG. 4 is indicated at 52 in FIG. 7 and at 54 in FIG. 7 for the simple equivalent circuit of FIG. 5. Although the true equivalent circuit (Figure 4) has better correlation than the simple equivalent circuit (Figure 5), for some applications this difference may not be significant.

The magnetic amplitude recovery method of the present invention is easily integrated into control systems for linear machines. Figure 8 illustrates a magnet amplitude recovery method that can be used to obtain piston amplitude in a beta type free piston Stirling cooler used to control the temperature of target 32. The displacer 38 moves synchronously with the movement of the piston 36, such that control of the piston movement will control the displacer movement. A linear motor 34 drives the piston 36 by mechanical connection to magnets 18. The amplitude of the piston movement must be controlled so that the moving parts do not collide with the mechanical stops 56 or 58. In the case of stop 58, displacer 38 will collide with the inner top of the machine if driven with excessive amplitude by piston 36. The difference between the set temperature 60 and the target temperature obtained by the temperature sensor 43 applied to both summing connections 62 provides an error signal to the controller 46. Controller 46 sets the voltage for driver 44, which provides input to linear motor 34. Driver 44 extracts the linear motor terminal current, voltage, and phase between voltage and current. These values are communicated to a microcomputer that processes the magnet amplitude recovery equations described above. As a result, the control system operates according to the following logic:

1. If the target temperature is higher than the set temperature, increase the piston amplitude by increasing the voltage (increase the cooling capacity). If the target temperature is lower than the set temperature, the piston amplitude is reduced by reducing the voltage.

2. Restore piston amplitude.

3. Compare the recovered piston amplitude with the stored set maximum amplitude.

4. If the recovered amplitude is greater than the set maximum amplitude, reduce the piston amplitude by reducing the voltage until the piston amplitude is no greater than the set maximum amplitude.

List of mathematical constants and variables and drawing symbols

α is the motor constant in units of volts per second per meter or newtons per ampere.

ω is the angular frequency of machine operation in radians per second.

X is the displacement amplitude of the armature and its component parts.

R _s represents the loss due to eddy current and hysteresis induced by the motion of magnets reciprocating in the gap caused by the winding open circuit.

R _dc represents the resistance loss of the coil.

ΔR _external represents the inductive loss in the surrounding structure of the motor.

R _ac represents the induced loss due to magnetic motion, which ties together the losses of R _s and R _dc .

L is the inductance of the motor mainly due to the coil windings.

V _ind is the open circuit voltage generated by the magnet motion (i.e. induced in the coil).

(V _ind ) _I is the phasor component of V _ind in the I direction.

(V _ind ) _L is the phasor component of V _ind in the L direction.

V _appl is the applied terminal voltage.

I and I _m are the terminal and motor currents, respectively.

jωL is the impedance of L.

10: Linear motor coil

11: reciprocating armature

12: iron core

13: Coil terminal

14: iron core air gap

15: Voltage applied to coil

16: Ring support structure

18: Permanent magnet (side by side segments or continuous ring)

20: outer part of the core

22: inner part of the core

24: Actual measured displacement amplitude

26: Recovered displacement amplitude [Figure 4, Equation 3-7]

28: Recovered displacement amplitude [Figure 5, Equations 4, 8, 9 and 7]

30: Free piston stirling cooler

32: Target (e.g. freezer)

34: Linear motor (Figure 8)

36: Stirling cooler piston

37: Stirling cooler cylinder

38: Sterling cooler displacer

40: Sterling cooler regenerator

42: Stirling cooler heat exchanger

43: Temperature sensor

44: driver circuit

46: controller

48: Piston amplitude (X) recovery

50: Displacement amplitude summation connection

52 : Recovered amplitude correlation for the equivalent circuit of Figure 4

54: Recovered amplitude correlation for the equivalent circuit of Figure 5

56: Mechanical stop that the Stirling cooler piston can hit.

58: Mechanical stop that the Stirling cooler displacer can hit.

60: set temperature

62: summation connection for temperature control

This detailed description, taken in conjunction with the drawings, is intended primarily as a detailed description of the presently preferred embodiments of the invention, and is not intended to represent the only form in which the invention may be configured or utilized. The detailed description presents the design, functionality, means and methods of implementing the invention in connection with the illustrated embodiments. However, the same or equivalent functions and features may be achieved by different embodiments, which are intended to be included within the spirit and scope of the present invention, and various modifications may be adopted without departing from the scope of the present invention or the following claims.

Claims (6)

A method for detecting the displacement amplitude ( and a stator wound around a ferromagnetic core with air gaps, the motor or alternator also having magnets fixed to the armature and positioned for reciprocating through the gaps, the motor or alternator also having a motor a constant (α), an equivalent resistance (R _dc ) representing the resistive losses in the coil, an equivalent resistance (ΔR _extemal ) representing inductive losses in structures surrounding the motor or alternator, and The method having an equivalent resistance (R _s ) representing the loss due to eddy current and hysteresis induced by the movement of the magnets,
(a) detecting the amplitude of alternating voltage (V _appl ) at the coil terminals;
(b) detecting the amplitude of alternating current (I) through the coil terminals;
(c) detecting a phase angle (ϕ _pf ) between the alternating voltage (V _appl ) and the alternating current (I);
(d) Equation calculating I _m according to;
(e) Equation calculating (V _ind ) _I according to;
(f) Equation calculating (V _ind ) _L according to; and
(g) Equation It includes calculating the displacement amplitude (X) according to
where ω is the radian frequency of V _appl . According to paragraph 1,
(a) determining a motor or alternator armature displacement amplitude (X _c ) at which the armature or a structure fixed to the armature collides with a fixed structure;
(b) selecting and storing a motor or alternator armature displacement amplitude (X _max ) that is less than X _c ;
(b) repeatedly performing the calculation of the displacement amplitude (X); and
(c) limiting the displacement amplitude of the motor or alternator to maintain displacement amplitude (X) ≤ X _max . A method for detecting the displacement amplitude ( and a stator wound around a ferromagnetic core with air gaps, the motor or alternator also having magnets fixed to the armature and positioned for reciprocating through the gaps, the motor or alternator also having a motor a constant (α), an equivalent resistance (R _ac ) representing the resistance losses in the coil and losses due to eddy currents and hysteresis induced by the movement of the magnets due to a coil open circuit, and a structure surrounding the motor or alternator. The method having an equivalent resistance (ΔR _extemal ) representing the inductive loss in
(a) detecting the amplitude of alternating voltage (V _appl ) at the coil terminals;
(b) detecting the amplitude of alternating current (I) through the coil terminals;
(c) detecting a phase angle (ϕ _pf ) between the alternating voltage (V _appl ) and the alternating current (I);
(d) Equation calculating (V _ind ) _I according to;
(e) Equation calculating (V _ind ) _L according to; and
(f) Equation It includes calculating the displacement amplitude (X) according to
where ω is the radian frequency of V _appl . According to paragraph 3,
(a) determining a motor or alternator armature displacement amplitude (X _c ) at which the armature or a structure fixed to the armature collides with a fixed structure;
(b) selecting and storing a motor or alternator armature displacement amplitude (X _max ) that is less than X _c ;
(b) repeatedly performing the calculation of the displacement amplitude (X); and
(c) limiting the displacement amplitude of the motor or alternator to maintain displacement amplitude (X) ≤ X _max . 1. A freezer comprising a reciprocating armature of alternating current, a free piston Stirling cooler mechanically connected to and driven by a linear motor, said linear motor comprising a coil having a pair of coil terminals and surrounding a ferromagnetic core with air gaps. The motor also has magnets fixed to the armature and positioned for reciprocating through the gaps, the motor also having a motor constant (α), an equivalent resistance representing the resistance loss in the coil. (R _dc ), the equivalent resistance (ΔR _extemal ) representing the induced losses in the structures surrounding the motor, and the equivalent resistance (ΔR extemal ) representing the losses due to eddy currents and hysteresis induced by the movement of the magnets by the coil open circuit. R _s ), the freezer having a motor controller,
(a) a voltage sensor connected to the coil terminals and configured to sense the amplitude of an alternating voltage (V _appl ) at the coil terminals;
(b) a current sensor connected in series with the coil terminals and configured to sense the amplitude of the alternating current (I) through the coil terminals;
(c) a phase detector circuit connected to the coil terminals and configured to sense a phase angle (ϕ _pf ) between the alternating voltage (V _appl ) and the alternating current (I); and
(d) (i) Equation Calculate I _m according to;
(ii) Mathematical formula Calculate (V _ind ) _I according to;
(iii) Mathematical formula Calculate (V _ind ) _L according to;
(iv) Mathematical formula Calculate the displacement amplitude (X) according to where ω is the radian frequency of V _appl ;
(v) a microcomputer circuit configured to limit the displacement amplitude (X) of the motor to be less than a selected and stored maximum displacement amplitude. 1. A freezer comprising a reciprocating armature of alternating current, a free piston Stirling cooler mechanically connected to and driven by a linear motor, said linear motor comprising a coil having a pair of coil terminals and surrounding a ferromagnetic core with air gaps. Having a stator wound on the an equivalent resistance (R _ac ) representing the loss due to eddy current and hysteresis induced by the movement of the magnets by the circuit, and an equivalent resistance (ΔR _extemal ) representing the induced loss in structures surrounding the motor or alternator. wherein the freezer has a motor controller,
(a) a voltage sensor connected to the coil terminals and configured to sense the amplitude of an alternating voltage (V _appl ) at the coil terminals;
(b) a current sensor connected in series with the coil terminals and configured to sense the amplitude of the alternating current (I) through the coil terminals;
(c) a phase detector circuit connected to the coil terminals and configured to sense a phase angle (ϕ _pf ) between the alternating voltage (V _appl ) and the alternating current (I); and
(d) (i) Equation Calculate (V _ind ) _I according to;
(ii) Mathematical formula Calculate (V _ind ) _L according to;
(iii) Mathematical formula Calculate the displacement amplitude (X) according to where ω is the radian frequency of V _appl ,
(iv) a microcomputer circuit configured to limit the displacement amplitude (X) of the motor to be less than a selected and stored maximum displacement amplitude.

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